Question

Two bicycles are sold for the same price, gaining 20% on one and losing 20% on the other. Find the cost price of each bicycle, if Rs.180 is lost in the whole transaction.

Answer 1

Let the S.P. of both the cycles be Rs. x each.
For the first cycle,
Profit = 20%
`"S.P."/"C.P." = 1 + "Profit"/(100)`

⇒ `x/"C.P." = 1 + (20)/(100)`

⇒ `x/"C.P." = (100 + 20)/(100)`

⇒ C.P. = `(100)/(120) x`

= `(5)/(6)x`
Profit
= S.P. - C.P.
= `x - (5)/(6) x`

= `((6 - 5)/(6))x`

= `x/(6)`
For the second cycle,
Loss = 20%
`"S.P."/"C.P." = 1 - "Loss"/(100)`

⇒ `x/"C.P." = 1 - (20)/(100)`

⇒ `x/"C.P." = (100 - 20)/(100)`

⇒ C.P. = `(100)/(80) x`

= `(5)/(4)x`
Loss 
= C.P. - S.P.
= `(5)/(4)x - x`

= `((5- 4)/(5))x`

= `x/(5)`
Given, total loss = Rs.180
⇒ `x/(4) - x/(6)` = 180

⇒ `(2x)/(24)` = 180
⇒ x = 12 x 180
= 2160
∴ C.P. of first bicycle
= `(5)/(6)x`

= `(5)/(6)` X Rs.2160
= Rs.1800

∴ C.P. of second bicycle 
= `(5)/(4)x`

= `(5)/(4)` x Rs.2160
= Rs.2700.